A method of allocation of Stokeslets and collocation points for the Boundary
Singularity Method (BSM) is proposed to solve Stokes flows about single
droplets and merging droplets settling on the surface of fibers in filtration
process using moderate number of singularities.
In the recent studies of optimal location of singularities for Stokes flows
about spherical rigid particles, the location of Stokeslets was determined as a
fraction of particle radius. The current study represents further extension to the
Stokeslet allocation schemes that was developed in order to evaluate Stokes
flowfield about single droplets and the \“peanut-shape” clusters of merging
droplets settling at relatively long cylindrical fibers. Three test problems are
solved to demonstrate capability of the BSM and proposed schemes of allocation
of singularities. The first problem is a cross-flow about cylindrical fiber with a
spherical droplet settling at its equatorial plane. This flow is modeled for a range
of ratios of droplet to fiber radii. The second problem is a cross-flow about
droplet on a fiber at the range of angles between flow and fiber corresponding to
position of droplet on fiber ranging from attached to equatorial point of fiber to
the back of fiber. The third problem is the BSM computation of Stokes force
exerted on a pair of merging droplets, one of which is sliding toward another
along the fiber.
Keywords: boundary singularity method, Stokes equations, microfluids,
Stokeslet, allocation of Stokeslets, droplet, fiber.